Bivariate splines for ozone concentration forecasting

In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed measurements and the functional linear regression model. We employ bivariate splines defined over triangulations of the relevant region of the USA to implement this functional data approach in which random surfaces represent ozone concentrations. We compare the least squares method with penalty to the principal components regression approach. Moderate sample sizes provide good quality forecasts in both cases with little computational effort. We also illustrate the variability of forecasts due to the choice of smoothing penalty. Finally, we compare our predictions with the ones obtained using thin-plate splines. Predictions based on bivariate splines require less computational time than the ones based on thin-plate splines and are more accurate. We also quantify the variability in the predictions arising from the variability in the sample using the jackknife, and report that predictions based on bivariate splines are more robust than the ones based on thin-plate splines.